Memristics: Memory is more than Storage
Memristive memory is able to surpass the conceptual limits of computational storage methods
Some orientation towards conceptual generalizations of memristive approaches is given with the use of poly-categorical methods.
"The biggest new news about memristors, though, came in a paper in Nature last week, in which HP announced that the devices can also perform logic functions. In other words, Wiliams said, a memristor can act as both a storage element and a logic element, or "a lock as well as a gate."
"There's nothing else I'm aware of that performs both of those functions simultaneously," he said.”
Williams said there is an "intriguing possibility" that if you could use the same structure to do actual computing as well as storage, you could send the program to where the data is and execute the problem where the data is stored. Of course, that all depends on what the performance of memristor-based devices ends up being, compared with traditional CPUs and memory systems.
"Note the double closure of the system which now recursively operates not only on what it “sees” but on its operators as well.”
(Heinz von Foerster, On constructing a Reality, in: Observing Systems, p. 305, 1984)
Memristive realizations are of second-order, they are not genuinely implemented by NAND-derivatives build by IMP but by a new kind of second-order construction. Because of their second-order status they are not primarily emulating storage but memory.
A finite state machine has a state but not a memory of a state.
A memristive machine has a state of a state, i.e. a meta-state as a memory, therefore a memristic machine is not a finite state machine.
A meta-state always can be taken as a simple state because a reduction from an as-abstraction to an is-abstraction is directly possible because the necessary informations are stored in the meta-state. From “x as y is z” there is an easy way to reduce it to “x is x”.